geoff planted dahlias in his garden. In the first year, geoffs garden produced 4 bulbs. In the second year it producted 8 bulbs, and in the third year it produced 16 bulbs. How many bulbs will Geoff have in the 10th year?
A: 2,048
B: 1,024
C: 40
D: 32
This is a geometric sequence with first term $4$ and common ratio $2$, since each year the number of bulbs doubles. Therefore, the $n$th term of the sequence is $4 \cdot 2^{n-1}$. So in the 10th year, we have $4 \cdot 2^{10-1} = 4 \cdot 2^9 = 2^{11} = \boxed{\textbf{(A) } 2,048}$.
To determine the number of bulbs Geoff will have in the 10th year, we can observe that the number of bulbs doubles each year.
First year: 4 bulbs
Second year: 4 * 2 = 8 bulbs
Third year: 8 * 2 = 16 bulbs
We can see a pattern here, where the number of bulbs doubles each year. Using this pattern, we can determine the number of bulbs in the 10th year by doubling the number of bulbs in the 9th year.
Ninth year: 16 * 2 = 32 bulbs
Tenth year: 32 * 2 = 64 bulbs
Therefore, Geoff will have 64 bulbs in the 10th year.
The correct answer is not listed among the options.